000101608 001__ 101608
000101608 005__ 20210902121724.0
000101608 0247_ $$2doi$$a10.1515/fca-2020-0025
000101608 0248_ $$2sideral$$a118189
000101608 037__ $$aART-2020-118189
000101608 041__ $$aeng
000101608 100__ $$aFerreira, E.M.
000101608 245__ $$aReflection properties of zeta related functions in terms of fractional derivatives
000101608 260__ $$c2020
000101608 5060_ $$aAccess copy available to the general public$$fUnrestricted
000101608 5203_ $$aWe prove that the Weyl fractional derivative is a useful instrument to express certain properties of the zeta related functions. Specifically, we show that a known reflection property of the Hurwitz zeta function ¿(n, a) of integer first argument can be extended to the more general case of ¿(s, a), with complex s, by replacement of the ordinary derivative of integer order by Weyl fractional derivative of complex order. Besides, ¿(s, a) with (s) > 2 is essentially the Weyl (s-2)-derivative of ¿(2, a). These properties of the Hurwitz zeta function can be immediately transferred to a family of polygamma functions of complex order defined in a natural way. Finally, we discuss the generalization of a recently unveiled reflection property of the Lerch''s transcendent.
000101608 536__ $$9info:eu-repo/grantAgreement/ES/DGA-UZ/E24-1$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2009-11154
000101608 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000101608 590__ $$a3.126$$b2020
000101608 591__ $$aMATHEMATICS$$b10 / 330 = 0.03$$c2020$$dQ1$$eT1
000101608 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b27 / 108 = 0.25$$c2020$$dQ1$$eT1
000101608 591__ $$aMATHEMATICS, APPLIED$$b22 / 265 = 0.083$$c2020$$dQ1$$eT1
000101608 592__ $$a1.397$$b2020
000101608 593__ $$aApplied Mathematics$$c2020$$dQ1
000101608 593__ $$aAnalysis$$c2020$$dQ1
000101608 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000101608 700__ $$aKohara, A.K.
000101608 700__ $$0(orcid)0000-0002-3837-8303$$aSesma, J.$$uUniversidad de Zaragoza
000101608 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica
000101608 773__ $$g23, 2 (2020), 520-533$$pFract. Calc. Appl. Anal.$$tFractional Calculus and Applied Analysis$$x1311-0454
000101608 8564_ $$s116661$$uhttps://zaguan.unizar.es/record/101608/files/texto_completo.pdf$$yPostprint
000101608 8564_ $$s1037749$$uhttps://zaguan.unizar.es/record/101608/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000101608 909CO $$ooai:zaguan.unizar.es:101608$$particulos$$pdriver
000101608 951__ $$a2021-09-02-09:30:55
000101608 980__ $$aARTICLE